# Analytic Evolution of Singular Distribution Amplitudes in QCD

## Abstract

Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.

- Authors:

- Old Dominion Univ., Norfolk, VA (United States)

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1346715

- Report Number(s):
- JLAB-PHY-14-2024; DOE/OR/23177-4100

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Thesis/Dissertation

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Tandogan Kunkel, Asli.
```*Analytic Evolution of Singular Distribution Amplitudes in QCD*. United States: N. p., 2014.
Web. doi:10.2172/1346715.

```
Tandogan Kunkel, Asli.
```*Analytic Evolution of Singular Distribution Amplitudes in QCD*. United States. doi:10.2172/1346715.

```
Tandogan Kunkel, Asli. Fri .
"Analytic Evolution of Singular Distribution Amplitudes in QCD". United States.
doi:10.2172/1346715. https://www.osti.gov/servlets/purl/1346715.
```

```
@article{osti_1346715,
```

title = {Analytic Evolution of Singular Distribution Amplitudes in QCD},

author = {Tandogan Kunkel, Asli},

abstractNote = {Distribution amplitudes (DAs) are the basic functions that contain information about the quark momentum. DAs are necessary to describe hard exclusive processes in quantum chromodynamics. We describe a method of analytic evolution of DAs that have singularities such as nonzero values at the end points of the support region, jumps at some points inside the support region and cusps. We illustrate the method by applying it to the evolution of a at (constant) DA, antisymmetric at DA, and then use the method for evolution of the two-photon generalized distribution amplitude. Our approach to DA evolution has advantages over the standard method of expansion in Gegenbauer polynomials [1, 2] and over a straightforward iteration of an initial distribution with evolution kernel. Expansion in Gegenbauer polynomials requires an infinite number of terms in order to accurately reproduce functions in the vicinity of singular points. Straightforward iteration of an initial distribution produces logarithmically divergent terms at each iteration. In our method the logarithmic singularities are summed from the start, which immediately produces a continuous curve. Afterwards, in order to get precise results, only one or two iterations are needed.},

doi = {10.2172/1346715},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Aug 01 00:00:00 EDT 2014},

month = {Fri Aug 01 00:00:00 EDT 2014}

}